Number of solutions of $8cosx$ = $x$ will be 

Let $\theta, 0 < \theta < \pi / 2$, be an angle such that the equation $x ^2+4 x \cos \theta+\cot \theta=0$ has equal roots for $x$. Then $\theta$ in radians is

If $\cos 3x + \sin \left( {2x - \frac{{7\pi }}{6}} \right) = - 2$, then $x = $ (where $k \in Z$)

If $\tan (\pi \cos \theta ) = \cot (\pi \sin \theta ),$ then the value of $\cos \left( {\theta - \frac{\pi }{4}} \right) =$

If $2\,cos\,\theta  + sin\, \theta \, = 1$ $\left( {\theta  \ne \frac{\pi }{2}} \right)$ , then $7\, cos\,\theta + 6\, sin\, \theta $ is equal to

If $\sin \theta = \sqrt 3 \cos \theta , - \pi < \theta < 0$, then $\theta = $